For why Philistine settlement in Canaan should be dated to the 1120s BC, see here.
As further evidence of this, it is best to explain the archaeological strata attributed to the phase between the first wave and second wave of Sea Peoples. The first wave of Sea Peoples is characterized by the destruction of Ugarit, which evidenced no Mycenaean IIIC in its destruction layer. According to the statements of Ramesses III, Amurru was laid waste to by the Sea Peoples, so he strengthened his frontier in Djahy. The Sea Peoples were defeated in both the Delta and Phoenicia. However, they may have caused disturbances in Philistia as well. The most notable event after their attempted invasion of the Egyptian Empire was the near-cessation of imports from the lands they conquered to Palestine.
Marine settlement did not end in Late Bronze III (the Lachish IV/ phase). Ashkelon remained inhabited. According to David Ussishkin, there is evidence that Lachish VI had contact with the sea (by means of Ashkelon, no doubt) by the fact marine fish bones were found in the stratum. However, no imported pottery whatsoever was found at Lachish VI, though much was found at Fosse Temple III. This begs the question of whether this lack of imported pottery was due to external or internal factors. It should be noted that, at the Egyptian stronghold of Beth-Shean, and, as Amihay Mazar mentioned, Tell Keisan and Acco, Mycenaean IIIc:1a pottery was found. On Cyprus, settlement patterns changed due to the migrations of the Sea Peoples, but they did not cease. It seems, therefore, that during Late Bronze III, all ports except Acco (to supply Egyptian soldiers at Beth-Shean) stopped importing wares associated with the Sea Peoples. Whether this was a voluntary choice by the Canaanite port cities or an involuntary decision forced upon them by Ramesses III cannot yet be known.